ADD results for does

tables/doe_ratio.tex

@@ -1,23 +1,23 @@
 
 % Table created by stargazer v.5.2.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
-% Date and time: Thu, Jul 29, 2021 - 04:15:57 PM
+% Date and time: Thu, Jul 29, 2021 - 05:45:05 PM
 \begin{tabular}{@{\extracolsep{5pt}}lc} 
 \\[-1.8ex]\hline 
 \hline \\[-1.8ex] 
 \\[-1.8ex] & CD4:CD8 CD62L+CCR7+ Ratio \\ 
 \hline \\[-1.8ex] 
- Dataset [2] & 893,357.900$^{***}$ \\ 
-  Functional mAb \% & 28,209.730$^{***}$ \\ 
-  IL2 Conc. (IU/ml) & 50,896.490$^{***}$ \\ 
-  DMS Conc. (1/ml) & 926.925$^{***}$ \\ 
-  Intercept & $-$3,368,762.000$^{***}$ \\ 
+ Dataset [2] & 0.020 \\ 
+  Functional mAb \% & 0.002$^{***}$ \\ 
+  IL2 Conc. (IU/ml) & 0.001 \\ 
+  DMS Conc. (1/ml) & 0.0001$^{***}$ \\ 
+  Intercept & $-$0.144$^{*}$ \\ 
  \hline \\[-1.8ex] 
 Observations & 30 \\ 
-R$^{2}$ & 0.835 \\ 
-Adjusted R$^{2}$ & 0.808 \\ 
-Residual Std. Error & 493,168.700 (df = 25) \\ 
-F Statistic & 31.571$^{***}$ (df = 4; 25) \\ 
+R$^{2}$ & 0.879 \\ 
+Adjusted R$^{2}$ & 0.860 \\ 
+Residual Std. Error & 0.039 (df = 25) \\ 
+F Statistic & 45.554$^{***}$ (df = 4; 25) \\ 
 \hline 
 \hline \\[-1.8ex] 
 \textit{Note:}  & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ 
-\end{tabular} 
+\end{tabular} 

tex/thesis.tex

@@ -50,6 +50,7 @@
 \newacronym{cpp}{CPP}{critical process parameter}
 \newacronym{dms}{DMS}{degradable microscaffold}
 \newacronym{doe}{DOE}{design of experiments}
+\newacronym{adoe}{ADOE}{adaptive design of experiments}
 \newacronym{gmp}{GMP}{Good Manufacturing Practices}
 \newacronym{cho}{CHO}{Chinese hamster ovary}
 \newacronym{all}{ALL}{acute lymphoblastic leukemia}
@@ -155,10 +156,12 @@
   \end{flushleft}
 }
 
+% a BME's best friend
 \newcommand{\invivo}{\textit{in vivo}}
 \newcommand{\invitro}{\textit{in vitro}}
 \newcommand{\exvivo}{\textit{ex vivo}}
 
+% various CD-whatever crap
 \newcommand{\cd}[1]{CD{#1}}
 \newcommand{\anti}[1]{anti-{#1}}
 \newcommand{\antih}[1]{anti-human {#1}}
@@ -180,17 +183,21 @@
 \newcommand{\ptcar}{\gls{car}+}
 \newcommand{\ptcarp}{\ptcar~\si{\percent}}
 
+% DOE responses I don't feel like typing ad-nauseam
+\newcommand{\pilII}{\gls{il2} concentration}
+\newcommand{\pdms}{\gls{dms} concentration}
+\newcommand{\pmab}{functional \gls{mab} surface density}
+
+% vendor and product stuff I don't feel like typing
 \newcommand{\catnum}[2]{(#1, #2)}
 \newcommand{\product}[3]{#1 \catnum{#2}{#3}}
-
 \newcommand{\thermo}{Thermo Fisher}
 \newcommand{\miltenyi}{Miltenyi Biotech}
 \newcommand{\bl}{Biolegend}
 
+% the obligatory misc category
 \newcommand{\inlinecode}{\texttt}
-
 \newcommand{\subcap}[2]{\subref{#1}) #2}
-
 \newcommand{\sigkey}{Significance test key: *p<0.1; **p < 0.05; ***p<0.01}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -2201,7 +2208,6 @@ between T cells. Since \gls{il2} is secreted by activated T cells themselves,
 T cells in the \gls{dms} system may need less or no \gls{il2} if this hypothesis
 were true.
 
-
 % TODO this plots proportions look dumb
 % TODO explain what the NLS lines are in b
 % TODO plot the differences in lower IL2 concentrations to better show this
@@ -2263,6 +2269,30 @@ at \SI{10}{\IU\per\ml} throughout the remainder of this aim.
   \input{../tables/doe_runs.tex}
 \end{table}
 
+% FIGURE first DOE results to show how the second DOE was motivated
+
+We conducted two consecutive \glspl{doe} to optimize the \pth{} and \ptmem{}
+responses for the \gls{dms} system. In the first \gls{doe} we, tested \pilII{} in
+the range of \SIrange{10}{30}{\IU\per\ml}, \pdms{} in the range of
+\SIrange{500}{2500}{\dms\per\ml}, and \pmab{} in the range of
+\SIrange{60}{100}{\percent}.
+
+% TODO explain why not all runs were used
+After performing the first \gls{doe} we augmented the original design matrix
+with an \gls{adoe} which was built with three goals in mind. Firstly we wished
+to validate the first \gls{doe} by assessing the strength and responses of each
+effect. Secondly, we wished to improve our confidence in regions that showed
+high complexity, such as the peak in the \gls{dms} concentration for the total
+\ptmem{} cell response. Thirdly, we wished to explore additional ranges of each
+response. Since \pilII{} and \pdms{} appeared to continue positively influence
+multiple responses beyond our tested range, we were curious if there was an
+optimum at some higher setting of either of these values. For this reason, we
+increased the \pilII{} to include \SI{40}{\IU\per\ml} and the \pdms{} to
+\SI{3500}{\dms\per\ml}. Note that it was impossible to go beyond
+\SI{100}{\percent} for the \pmab{}, so runs were positioned for this parameter
+with validation and confidence improvements in mind. The runs for each \gls{doe}
+were shown in \cref{tab:doe_runs}.
+
 \begin{figure*}[ht!]
   \begingroup
 
@@ -2316,6 +2346,57 @@ at \SI{10}{\IU\per\ml} throughout the remainder of this aim.
   \input{../tables/doe_ratio.tex}
 \end{table}
 
+The response plots from both \glspl{doe} are shown in \cref{fig:doe_responses}
+for total \ptmem{} cells, total \pth{} cells, total \ptmemh{} cells, and CD4:CD8
+ratio in the \ptmem{} compartment. In general, the responses for the first and
+second \gls{doe} seemed to overlap, although not perfectly. Interestingly, only
+the \ptmem{} response seemed to have anything more complex than a linear
+relationship, particularly in the case of \pilII{} and \pdms{}, which showed
+intermediate optimums (\cref{fig:doe_responses_mem}). In the case of \pilII{},
+it was not clear if this optimum was simply due to a batch effect of being from
+the first or second \gls{doe}. The optimum for \pdms{} appeared in the same
+location albeit more pronounced in the second \gls{doe} so, giving more
+confidence to the location of this second order feature. The remainder of the
+responses showed mostly linear relationships in all parameter cases
+(\cref{fig:doe_responses_cd4,fig:doe_responses_mem4,fig:doe_responses_ratio}).
+
+% TODO it seems arbitrary that I went straight to a third order model, the real
+% reason is because it seemed weird that a second order model didn't find
+% anything to be significant
+We performed linear regression on the three input parameters as well as a binary
+parameter representing if a given run came from the first or second \gls{doe}
+(called `dataset'). Starting with the total \ptmem{} cells response, we fit a
+first order regression model using these four parameters
+(\cref{tab:doe_mem1.tex}). While \pilII{} was found to be a significant
+predictor, the model fit was extremely poor ($R^2$ of 0.331). This was not
+surprising given the apparent complexity of this response
+(\cref{fig:doe_responses_mem}). To obtain a better fit, we added second and
+third degree terms (\cref{tab:doe_mem2.tex}). Note that the dataset parameter
+was not included in the second order interaction as this was treated as a
+blocking variable, which are typically not assumed to have interaction effects.
+Also note that the response was log-transformed, which yielded a better fit. In
+this model many more parameters emerged as being significant, including the
+quadratic terms for \pdms{} and \pilII{}, in agreement with what can be
+qualitatively observed in the response plot (\cref{fig:doe_responses_mem}).
+Furthermore, the dataset parameter was weakly significant, indicating a possible
+batch effect between the \glspl{doe}. We should also note that despite many
+parameters being significant, this model was still only mediocre in describing
+this response; the $R^2$ was 0.741 but the adjusted $R^2$ was 0.583, indicating
+that our data might be underpowered for a model this complex. Further
+experiments beyond what was performed here may be needed to fully describe this
+response.
+
+% TODO combine these tables into one
+We performed linear regression on the other three responses, all of which
+performed much better than the \ptmem{} response as expected given the much
+lower apparent complexity in the response plots
+(\cref{fig:doe_responses_cd4,fig:doe_responses_mem4,fig:doe_responses_ratio}).
+All these models appeared to fit will, with $R^2$ and adjusted $R^2$ upward of
+0.8. In all but the CD4:CD8 \ptmem{} ratio, the dataset parameter emerged as
+significant, indicating a batch effect between the \glspl{doe}. All other
+parameters except \pilII{} in the case of CD4:CD8 \ptmem{} ratio were
+significant predictors.
+
 \begin{figure*}[ht!]
   \begingroup
 
@@ -2330,9 +2411,17 @@ at \SI{10}{\IU\per\ml} throughout the remainder of this aim.
     \subcap{fig:doe_sr_contour_ratio}{CD4:CD8 ratio in the \ptmem{}
       compartment}.
   }
-  \label{fig:doe_responses}
+  \label{fig:doe_sr_contour}
 \end{figure*}
 
+We then visualized the total \ptmemh{} cells and CD4:CD8 \ptmem{} ratio using
+the response explorer in DataModeler to create contour plots around the maximum
+responses. For both, it appeared that maximizing all three input parameters
+resulted in the maximum value for either response (\cref{fig:doe_responses}).
+While not all combinations at and around this optimum were tested, the model
+nonetheless showed that there were no other optimal values or regions elsewhere
+in the model.
+
 % TODO this section header sucks
 \subsection{AI modeling reveals highly predictive species}